Here are the essential concepts you must grasp in order to answer the question correctly.
Radical Equations
Radical equations are equations that involve a variable within a radical (square root, cube root, etc.). To solve these equations, one typically isolates the radical on one side and then raises both sides of the equation to the power that eliminates the radical. This process may introduce extraneous solutions, so it's important to check all potential solutions in the original equation.
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Isolating the Variable
Isolating the variable is a fundamental algebraic technique used to solve equations. This involves rearranging the equation to get the variable on one side and all other terms on the opposite side. In the context of radical equations, isolating the radical before squaring both sides is crucial for correctly solving the equation.
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Equations with Two Variables
Extraneous Solutions
Extraneous solutions are solutions that emerge from the process of solving an equation but do not satisfy the original equation. This is particularly common in radical equations, where squaring both sides can introduce solutions that are not valid. Therefore, it is essential to substitute any found solutions back into the original equation to verify their validity.
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